What happens if we aggregate both the supply and demand over a second (and don't allow price resolution smaller than a cent), then each seller gets to sell a portion of the demand proportional to the amount of this stock he owns?

This seems to disincentivize putting up for sale more than the seller wants to sell, and to also disincentivize "Sybil attacks" where the seller has an incentive to create false identities for himself. (Just a thought experiment, would be happy to know what I'm missing here :-)